TRS Standard pair #615303217

details

property	value
status	complete
benchmark	#3.55.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	2.89919781685 seconds
cpu usage	9.778758884
max memory	9.90711808E8

stage attributes

key	value
output-size	85283
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 app'(app'(minus(),x),0()) -> x
 app'(app'(minus(),app'(s(),x)),app'(s(),y)) -> app'(app'(minus(),x),y)
 app'(app'(quot(),0()),app'(s(),y)) -> 0()
 app'(app'(quot(),app'(s(),x)),app'(s(),y)) ->
 app'(s(),app'(app'(quot(),app'(app'(minus(),x),y)),app'(s(),y)))
 app'(app'(le(),0()),y) -> true()
 app'(app'(le(),app'(s(),x)),0()) -> false()
 app'(app'(le(),app'(s(),x)),app'(s(),y)) -> app'(app'(le(),x),y)
 app'(app'(app(),nil()),y) -> y
 app'(app'(app(),app'(app'(add(),n),x)),y) -> app'(app'(add(),n),app'(app'(app(),x),y))
 app'(app'(low(),n),nil()) -> nil()
 app'(app'(low(),n),app'(app'(add(),m),x)) ->
 app'(app'(app'(if_low(),app'(app'(le(),m),n)),n),app'(app'(add(),m),x))
 app'(app'(app'(if_low(),true()),n),app'(app'(add(),m),x)) ->
 app'(app'(add(),m),app'(app'(low(),n),x))
 app'(app'(app'(if_low(),false()),n),app'(app'(add(),m),x)) -> app'(app'(low(),n),x)
 app'(app'(high(),n),nil()) -> nil()
 app'(app'(high(),n),app'(app'(add(),m),x)) ->
 app'(app'(app'(if_high(),app'(app'(le(),m),n)),n),app'(app'(add(),m),x))
 app'(app'(app'(if_high(),true()),n),app'(app'(add(),m),x)) -> app'(app'(high(),n),x)
 app'(app'(app'(if_high(),false()),n),app'(app'(add(),m),x)) ->
 app'(app'(add(),m),app'(app'(high(),n),x))
 app'(quicksort(),nil()) -> nil()
 app'(quicksort(),app'(app'(add(),n),x)) ->
 app'(app'(app(),app'(quicksort(),app'(app'(low(),n),x))),app'(app'(add(),n),
                                                               app'(quicksort(),
                                                                    app'
                                                                    (app'(high(),n),x))))
 app'(app'(map(),f),nil()) -> nil()
 app'(app'(map(),f),app'(app'(add(),x),xs)) -> app'(app'(add(),app'(f,x)),app'(app'(map(),f),xs))
 app'(app'(filter(),f),nil()) -> nil()
 app'(app'(filter(),f),app'(app'(add(),x),xs)) ->
 app'(app'(app'(app'(filter2(),app'(f,x)),f),x),xs)
 app'(app'(app'(app'(filter2(),true()),f),x),xs) -> app'(app'(add(),x),app'(app'(filter(),f),xs))
 app'(app'(app'(app'(filter2(),false()),f),x),xs) -> app'(app'(filter(),f),xs)

Proof:
 Extended Uncurrying Processor:
  application symbol: app'
  symbol table:
   filter2 ==> filter20/0 filter21/1 filter22/2 filter23/3 filter24/4
   filter ==> filter0/0 filter1/1 filter2/2
   map ==> map0/0 map1/1 map2/2
   quicksort ==> quicksort0/0 quicksort1/1
   if_high ==> if_high0/0 if_high1/1 if_high2/2 if_high3/3
   high ==> high0/0 high1/1 high2/2
   if_low ==> if_low0/0 if_low1/1 if_low2/2 if_low3/3
   low ==> low0/0 low1/1 low2/2
   add ==> add0/0 add1/1 add2/2
   nil ==> nil0/0
   app ==> app0/0 app1/1 app2/2
   false ==> false0/0
   true ==> true0/0
   le ==> le0/0 le1/1 le2/2
   quot ==> quot0/0 quot1/1 quot2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   minus ==> minus0/0 minus1/1 minus2/2
   
  uncurry-rules:
   app'(minus1(x6),x7) -> minus2(x6,x7)
   app'(minus0(),x6) -> minus1(x6)
   app'(s0(),x10) -> s1(x10)
   app'(quot1(x12),x13) -> quot2(x12,x13)
   app'(quot0(),x12) -> quot1(x12)
   app'(le1(x15),x16) -> le2(x15,x16)
   app'(le0(),x15) -> le1(x15)
   app'(app1(x20),x21) -> app2(x20,x21)
   app'(app0(),x20) -> app1(x20)
   app'(add1(x24),x25) -> add2(x24,x25)
   app'(add0(),x24) -> add1(x24)
   app'(low1(x27),x28) -> low2(x27,x28)
   app'(low0(),x27) -> low1(x27)
   app'(if_low2(x30,x31),x32) -> if_low3(x30,x31,x32)
   app'(if_low1(x30),x31) -> if_low2(x30,x31)
   app'(if_low0(),x30) -> if_low1(x30)
   app'(high1(x34),x35) -> high2(x34,x35)
   app'(high0(),x34) -> high1(x34)
   app'(if_high2(x37,x38),x39) -> if_high3(x37,x38,x39)
   app'(if_high1(x37),x38) -> if_high2(x37,x38)
   app'(if_high0(),x37) -> if_high1(x37)
   app'(quicksort0(),x41) -> quicksort1(x41)
   app'(map1(x43),x44) -> map2(x43,x44)
   app'(map0(),x43) -> map1(x43)
   app'(filter1(x46),x47) -> filter2(x46,x47)
   app'(filter0(),x46) -> filter1(x46)
   app'(filter23(x49,x50,x51),x52) -> filter24(x49,x50,x51,x52)
   app'(filter22(x49,x50),x51) -> filter23(x49,x50,x51)
   app'(filter21(x49),x50) -> filter22(x49,x50)
   app'(filter20(),x49) -> filter21(x49)
  eta-rules:

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